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Write the slope-intercept form of the equation of the line described: Through (-5, -1), perpendicular to y = -2x - 1.

User Barker
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Final answer:

The slope-intercept form of the equation of the line perpendicular to y = -2x - 1 through (-5, -1) is y = 1/2(x + 5) - 1.

Step-by-step explanation:

To find the equation of a line perpendicular to a given line, we need to find its slope. The given line has a slope of -2. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line is 1/2.

Using the point-slope form of the equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can plug in the coordinates (-5, -1) and the slope of 1/2 to get:

y - (-1) = 1/2(x - (-5))

Simplifying, we get y + 1 = 1/2(x + 5).

Further simplifying, we end up with the slope-intercept form of the equation:

y = 1/2(x + 5) - 1

User Endline
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